Question

“the perimeter of the rectangle below is 90 units. find the length of side PS. write your answer without variables.”

Answer 1

19

Explanation:

The opposite sides are equal, so:

PS = 3y+1

RS = 4y+2

QR = 3y+1

PQ = 4y+2

Therefore, we can set the perimeter 90 = PS+RS+QR+PQ

90 = (3y+1) + (4y+2) + (3y+1) + (4y+2), or,

90 = 2(3y+1) + 2(4y+2)

90 = 6y+2 + 8y+4

90 = 14y + 6

84 = 14y

y = 6

Then, we go back to the question. It's asking for the length of PS. PS = 3y+1, so we plug in 6 for y

3(6)+1

18 + 1 = 19